Why is Amazon paying for more exclusive content? Topeka Capital
analysts Victor Anthony explains it in one paragraph:

Amazon's successful foray into devices (e-Readers, tablets,
streaming boxes, and a rumored phone) is about driving digital
media content sales, but also about driving customers to Amazon
Prime, whose members purchase more frequently and in greater
dollar amount than non-members. The addition of HBO's content to
Prime Instant Video should attract the binge watch fanatics,
drive more Prime members, and lead to lower churn. This is a win
for Amazon.

Amazon Prime, with "at least 20 million"
subscribers, is about more than just video. It
includes free two-day shipping for many items on the site. Prime
members tend to spend significantly more money than non-Prime
members.

By beefing up its video content, Amazon is making Prime
subscriptions more attractive to potential members, and the more
people who sign up for Prime, the better for Amazon.

Disclosure: Jeff Bezos is an investor in Business Insider through his
personal investment company Bezos Expeditions.